Allocation of Prizes in Contests with Participation Constraints

• DOI: http://doi.org/10.1111/jems.12030
• Author: Aner Sela,Reut Megidish
• Date: 01 December 2013
• Published date: 01 December 2013

Allocation of Prizes in Contests with Participation

Constraints

REUT MEGIDISH

Managing Human Resources

Sapir Academic College

D.N. Hof Ashkelon 79165, Israel

reutmeg@gmail.com

ANER SELA

Economics Department

Ben-Gurion University of Negev

Beer-Sheva 84105, Israel

anersela@bgu.ac.il

We study all-pay contests with an exogenous minimal effort constraint where a player can

participate in a contest only if his effort (output) is equal to or higher than the minimal effort

constraint. Contestants are privately informed about a parameter (ability) that affects their cost

of effort. The designer decides about the size and number of prizes. We analyze the optimal

prize allocation for the contest designer who wishes to maximize either the total effort or the

highest effort. It is shown that if the minimal effort constraint is relatively high, the winner-

take-all contest in which the contestant with the highest effort wins the entire prize sum does

not maximize the expected total effort or the expected highest effort. Rather, a random contest

in which the entire prize sum is equally allocated to all the participants yields a higher expected

total effort as well as a higher expected highest effort.

1. Introduction

Contests are situations in which agents spend resources in order to win one or more

prizes. Their main feature is that, independently of success, all contestants bear some

costs. In the all-pay contest with a single prize, for example, the contestant with the

highest effort (output) wins the entire prize, but all the contestants bear the cost of their

effort.1Numerous applications of the all-pay contest have been made to rent-seekingand

lobbying in organizations, R&D races, political contests, promotions in labor markets,

trade wars, military and biological wars of attrition.

Most of the literature on contest theory, especially on all-pay contests, has focused

on the issue of the optimal allocation of prizes when the contestants do not face any

participation constraint. As Moldovanu and Sela (2001,2006) showed, in all-pay contests

under incomplete information and without participation constraints, the winner-take-

all structure in which the contestant with the highest effort (output) wins the entire

prize sum is usually the optimal architecture for maximizing the contestants’ expected

total effort.2However, in real-life contests, the contestants usually face participation

1. The all-pay contest (auction) has been studied, among others, by Hilman and Reiley (1989), Baye et al.

(1993,Bayeetal.1996), and Che and Gale (1998,2000).

2. In a similar vein, Schweinzer and Segev (2012) demonstrated that the optimal prize structure of sym-

metric n-player Tullock tournaments assigns the entire prize sum to the winner, provided that a symmetric

C2013 Wiley Periodicals, Inc.

Journal of Economics & Management Strategy, Volume22, Number 4, Winter 2013, 713–727